Using Gosu language I have implemented a very basic Neural Network Program to train networks based on Stochastic Gradient Descent, Fully Connected Layers and Sigmoid Neurons.
You can train the neural network to understand any function! However this implementation is not parallelized, so huge inputs will make it slow to learn. I am using it as a playground to learn about NN and Gosu so I designed it in a way that adding new types of neurons and layers would be easy.